Optical fiber technology is found in a wide variety of applications to flexibly relay light between two points, enabling information transfer across long distances and allowing access to hard-to-reach areas. Large-core optical fibers and light guides find frequent use in illumination and spectroscopic applications, for example, endoscopy and high-resolution astronomical spectroscopy. Proper alignment is critical for maximizing throughput in optical fiber coupling systems; however, there currently are no formal approaches to tolerancing the alignment of a lightguide coupling system. Here, we propose a Fourier alignment sensitivity (FAS) algorithm to determine the optimal tolerances on the alignment of a light guide by computing the alignment sensitivity. The algorithm shows excellent agreement with both simulated and experimentally measured values and improves on the computation time of equivalent ray-tracing simulations by two orders of magnitude. We then apply FAS to tolerance and fabricate a coupling system, which is shown to meet specifications, thus validating FAS as a tolerancing technique. These results indicate that FAS is a flexible and rapid means to quantify the alignment sensitivity of a light guide, widely informing the design and tolerancing of coupling systems.